The government said yesterday that the Social Security tax will apply next year to the first $32,400 of an individual's earnings, up from $29,700 this year.

Under the law the amount of income subject to the tax rises automatically each year with inflation.

The Social Security tax rate is also scheduled to increase fractionally Jan. 1, from the current 6.65 percent each for employer and employe to 6.7 percent.

The combined effect of these increases in base and rate will be to lift the maximum Social Security tax next year by nearly 10 percent, or $195.75, to $2,170.80 per employe.

The increase in earnings subject to tax is $300 more than either the Reagan or Carter administraions had predicted.

For the average worker making $13,729 this year and $15,045 next year, the tax will grow by just under $100, from $912.98 to $1,008.02, according to the Social Security Administration.

The tax increases were voted in 1977 in legislation that was supposed to leave all three of the Social Security trust funds solvent. They pay retirement and disability benefits and, through Medicare, the medical bills of about one American in seven.

The program remains in financial trouble, however, and has been a major issue between the major political parties this year. The Reagan administration at one point proposed major cuts in benefits which both Democrats and some Republicans said were unneeded, and the president has now withdrawn.

Congress is about to pass more modest legislation to keep the program going while it decides what else it needs to do.

For self-employed persons, the Social Security tax rate will rise from 9.3 percent to 9.35 percent next year. The effect, when combined with the increase in the earnings base to $32,400, will mean the maximum possible Social Security tax for those persons will jump to $3,029.40, an increase of $267.30.

Among other changes to go into effect Jan. 1:

* The maximum earnings a beneficiary under 65 can earn without losing benefits will grow from $4,080 to $4,440.

* The ceiling on exempt earnings for persons aged 65 to 72 will grow from $5,500 to $6,000.

* The amount of quarterly earnings to qualify for coverage will increase from $310 to $340.